Explicit Formulas for Orthogonal IIR Wavelets

Explicit solutions are given for the rational function P (z) for two classes of IIR orthogonal 2-band wavelet bases, for which the scaling lter is maximally at. P (z) denotes the rational transfer function H(z)H(1=z) where H(z) is the (lowpass) scaling lter. The rst is the class of solutions that are intermediate , between the Daubechies and the Butterworth wavelets. It is found that the Daubechies, the Butterworth, and the intermediate solutions are uniied by a single formula. The second is the class of scaling lters realizable as a parallel sum of two allpass lters (a particular case of which yields the class of symmetric IIR orthogonal wavelet bases). For this class, an explicit solution is provided by the solution to an older problem in group delay approximation by digital allpole lters.